Couldn't the invisibility cloak be used to sneak out baby Harry when Voldemort finds out Harry's location? If yes, then why did James let Dumbledore borrow it? Also the question can be: why did Dumbledore borrow it knowing that baby Harry's life was in danger?
It seems like plot convenience to me that Dumbledore had conveniently borrowed the cloak to examine it exactlyat the time when James needed it the most. Is there a good reason for this?